A non-empty set of elements G is said to form a

groupoid if in G is defined a binary operation called the product denoted by * such that a * b [member of] G, [for all] a, b [member of] G.

Keywords: frozen accident, rate distortion function, protein folding, free energy density, spin glass,

groupoid, Onsager relations, holonomy

An Abel- Grassmann's

groupoid, abbreviated as an AG-

groupoid (or in some papers left almost semigroup), is a non-associative algebraic structure mid way between a

groupoid and a commutative semigroup.

NIS TO R, Analysis ofgeometric operators on open manifolds: a

groupoid approach, in Quantization of Singular Symplectic Quotients, N.

c], and they turn out to be automorphisms of the Einstein

groupoid ([R.

Heller's current work focuses on the fields of noncommutative geometry and

groupoid theory in mathematics.

Definition 1: An ordered pair (S, -), with S a non-empty set and - being a binary operation on S, is called a subtractive

groupoid if (1.

By Theorem 5, P is a

groupoid, where the inverse of a morphism [P] : T [right arrow] S is [[P.

Define a binary operation (*) on L: if x * y [member of] L for all x,y [member of] L, (L,*) is called a

groupoid.

For example one may think of X/G as the

groupoid whose set of objects is X and with morphisms given by X/G(a, b) = {g [member of] G|ga = b} for a,b [member of] G.

Keywords: global workspace, entropy, cognition, rate distortion function, giant component,

groupoid, stochastic resonance.

Smarandache

Groupoids exhibit simultaneously the properties of a semigroup and a

groupoid.